# Triangle calculator - result

You have entered perimeter p and aspect ratio a:b:c = 6:5:3.

### Obtuse scalene triangle.

Sides: a = 9   b = 7.5   c = 4.5

Area: T = 16.83774582405
Perimeter: p = 21
Semiperimeter: s = 10.5

Angle ∠ A = α = 93.82325537293° = 93°49'21″ = 1.63875124752 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 29.92664348666° = 29°55'35″ = 0.52223148218 rad

Height: ha = 3.74216573868
Height: hb = 4.49899888641
Height: hc = 7.48333147735

Median: ma = 4.24326406871
Median: mb = 6.04766933112
Median: mc = 7.97326093596

Vertex coordinates: A[4.5; 0] B[0; 0] C[5; 7.48333147735]
Centroid: CG[3.16766666667; 2.49444382578]
Coordinates of the circumscribed circle: U[2.25; 3.9098695663]
Coordinates of the inscribed circle: I[3; 1.60435674515]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 86.17774462707° = 86°10'39″ = 1.63875124752 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad

# How did we calculate this triangle?

### 1. Input data entered: perimeter p and aspect ratio a:b:c. ### 2. From side a we calculate T: ### 3. From side a and angle β we calculate height hc: Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. ### 4. The triangle circumference is the sum of the lengths of its three sides ### 5. Semiperimeter of the triangle ### 6. The triangle area using Heron's formula ### 7. Calculate the heights of the triangle from its area. ### 8. Calculation of the inner angles of the triangle using a Law of Cosines    